非饱和土中桩的动力响应与循环荷载试验研究
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摘要
摘要：桩的动力响应研究是桩支承建筑物抗震设计和桩基完整性检测的理论基础。由于问题的复杂性,已往研究大多将桩侧土简化为单相或饱和两相弹性介质。众所周知,工程环境所处的近地表土层往往处于非饱和状态,为固、液、气三相的多孔介质材料。因此,本文在非饱和土动力学最新研究成果的基础上,基于三相多孔介质波动方程,充分考虑各相材料间的惯性和粘性耦合效应以及毛细压力作用,通过理论分析和模型试验对非饱和土-桩动力相互作用问题,非饱和土弹性半空间中埋置振源时的基本解以及桩的长期荷载循环特性进行了系统的研究,主要研究内容包括以下几个方面：
(1)针对半空间埋置振源下的三维Lamb问题,运用方位角的Fourier级数展开和径向Hankel变换技术,直接对频域内的非饱和土波动方程进行求解,并结合地基表面的边界条件以及荷载作用面上的连续性条件,求得了非饱和均质弹性半空间内部作用任意振源时的动力Green函数,退化到饱和土中的解与已有文献的结果相吻合。
(2)考虑基质吸力对土体动剪切模量的影响,建立了竖向简谐振动作用下非饱和土和单桩耦合动力响应模型,求解了轴对称条件下非饱和土体的动力控制方程和基桩的一维波动方程,根据桩土界面衔接条件以及桩端不同支承形式,给出了嵌岩桩和非端承桩的桩顶复动刚度、速度导纳以及土层阻抗在频域内的解答。
(3)通过Helmholtz矢量分解及分离变量法解耦波动方程,并将桩等效为能考虑其剪切变形的Timoshenko杆件,采用Novak三维连续介质模型对非饱和土中端承桩的稳态水平振动进行了研究；同时利用半空间水平动力Green函数,建立了非饱和土中水平受荷单桩的Fredholm积分方程,得到了单桩动力阻抗的封闭形式解答,考察了桩身位移、弯矩和剪力沿深度的分布规律。
(4)在Novak平面应变模型的基础上,利用散射域中的水平位移衰减函数,通过位移场的叠加考虑桩-桩间的波动干扰和群桩效应,推导了水平稳态谐振下非饱和土中单桩及群桩基础的阻抗函数以及各单桩分担的荷载,并讨论了饱和度、频率和桩间距等参数对基础振动特性的影响。
(5)推导了两种不混溶流体饱和多孔介质中Rayleigh波的弥散特征方程,讨论了波速、自由场位移分布及粒子运动轨迹,随后在求得非饱和土半空间自由波场解的基础上,采用Winkler地基梁模型,考虑上部结构惯性力的作用,对频域内全埋入单桩和部分埋入单桩在Rayleigh波作用下的横向动力响应进行了研究,分析了饱和度、轴向荷载和自由段桩长等因素与桩的地震反应之间的相互影响关系。
(6)通过开展红黏土中单桩轴向循环荷载模型试验,对不同循环荷载比和加载频率下桩的长期动力特性进行了研究,并从桩侧土剪切刚度和侧阻退化两方面出发,对循环荷载作用下桩顶累积沉降机理进行了分析。在FLAC3D中,实现了能够反映剪切刚度疲劳退化的修正Hardin-Drnevich(H-D)模型,并对常法向刚度(CNS)循环剪切下侧阻退化进行了数值模拟。
Abstract:Pile dynamics is the theoretical basis of both seismic design for building supporting by piles and integrity testing of piles. Owing to the complexity of the problem, the soils were usually assumed to be single-phase or saturated two-phase elastic medium for simplicity in the past studies. As we know, the near-surface soil existing in engineering environment is mostly unsaturated, and consists of three-phase system: solid skeleton and pores, with water and air filled in the pores. Based on the theoretical framework of unsaturated soil, and following the motion equations for multiphase porous media, the soil-pile dynamic interaction, the fundamental solution of internal dynamic source in a semi-infinite unsaturated elastic medium, and the deformation characteristics of pile subjected to cyclic loading are investigated in this paper via analytical and experimental studies. The viscous and inertial couplings between each phase together with the capillary pressure are taken into account during the process of derivation. The main contents of this thesis are listed as follows:
(1) The three dimensional lamb's problem under consideration is to determine the motion of an unsaturated poroelastic half-space subjected to internal excitation. By the application of the techniques of Fourier expansion and Hankel integral transforms with respect to the circumferential and radial coordinates, respectively, the general solution of the governing partial differential equations in the transformed domain is obtained. Furthermore, the closed form Green's functions of an unsaturated homogeneous elastic half-space to an arbitrary internal harmonic loading is derived, with consideration of the boundary conditions of the surface and the continuity conditions at the depth of loading. The formulas developed are confirmed in comparison with the degenerated solution of saturated soil.
(2) Considering the effect of matric suction on the dynamic shear modulus, the interaction model between the unsaturated soil and single pile under vertical harmonic motion is proposed. The resistance factor and vibration modes of soil layer are first obtained from the direct decoupling of the governing equations under axisymmetric conditions. On the basis of the assumptions of perfect contact along the pile-soil and the supporting types at the pile tip (rigid bearing or Winkler model), the motion equation of the pile treated as a bar and described by the conventional1-D structure vibration theory is then solved. The complex stiffness at the top of the pile, the velocity mobility together with the soil impedances in the frequency domain are derived ultimately.
(3) By virtue of the Helmholtz decomposition and variable separation method to the decoupling of motion equation, the dynamic characteristics for the horizontal vibration of an end-bearing pile in unsaturated soil are investigated through the three-dimensional continuum model proposed by Novak. The bending, shearing effects of pile are accounted for by modeling the pile as a Timoshenko beam. Moreover, utilizing the dynamic Green's function for unsaturated half-space under interior horizontal disk loading, the second kind of Fredholm integral equations describing the dynamic response of the laterally loaded single pile are established via the fictitious pile method. The semi-analytical solutions for dynamic stiffness of the pile head are developed in the frequency domain, and the distributions of pile displacement, bending moment and shear force along the depth are examined.
(4) With the Novak plain strain model, approximate dynamic impedance of single pile subjected to lateral vibration is first derived within the framework of wave theory of three-phase porous medium. A modified attenuation function of horizontal movements in scattering domain is then obtained, and the response of single pile is further extended to pile groups by employing the principle of superstition based on pile-pile interaction factor. On the basis of the developed solutions, the effects of parameters including the saturation, the excitation frequency and the pile spacing on the dynamic behavior as well as the load sharing are studied.
(5) The dispersion equations of Rayleigh waves in a porous medium saturated by two immiscible viscous fluids are deduced, and the variations of wave velocity, displacement distribution of free field and particle motion are discussed with the changes of soil properties. And then, considering the inertia effect of the superstructures, and within the obtained wave field solution for unsaturated soil half space, closed-form expressions for transverse seismic performance are presented through a dynamic Winkler model, for both fully-buried and partially-buried single pile in the unsaturated soil excited by incident Rayleigh waves. In addition, the influences of the saturation, the axial loading and the pile length of extended segment on the seismic response of pile are determined through numerical calculation.
(6) The performance of small-scale model piles embedded into red clay and tested under cyclic axial loadings is presented. The influences of cyclic loading levels and rates on long-term dynamic behaviors of pile are observed, and the mechanics of accumulated settlement is analyzed from the views of shear stiffness softening and skin friction degradation. Furthermore, the modified Hardin-Drnevich (H-D) model, being capable of reflecting the fatigue degradation of shear stiffness, is achieved in the FLAC3D, and the behavior of shear resistance degradation during quasi-static cyclic shearing under constant normal stiffness (CNS) condition is numerically investigated.
(1)针对半空间埋置振源下的三维Lamb问题,运用方位角的Fourier级数展开和径向Hankel变换技术,直接对频域内的非饱和土波动方程进行求解,并结合地基表面的边界条件以及荷载作用面上的连续性条件,求得了非饱和均质弹性半空间内部作用任意振源时的动力Green函数,退化到饱和土中的解与已有文献的结果相吻合。
(2)考虑基质吸力对土体动剪切模量的影响,建立了竖向简谐振动作用下非饱和土和单桩耦合动力响应模型,求解了轴对称条件下非饱和土体的动力控制方程和基桩的一维波动方程,根据桩土界面衔接条件以及桩端不同支承形式,给出了嵌岩桩和非端承桩的桩顶复动刚度、速度导纳以及土层阻抗在频域内的解答。
(3)通过Helmholtz矢量分解及分离变量法解耦波动方程,并将桩等效为能考虑其剪切变形的Timoshenko杆件,采用Novak三维连续介质模型对非饱和土中端承桩的稳态水平振动进行了研究；同时利用半空间水平动力Green函数,建立了非饱和土中水平受荷单桩的Fredholm积分方程,得到了单桩动力阻抗的封闭形式解答,考察了桩身位移、弯矩和剪力沿深度的分布规律。
(4)在Novak平面应变模型的基础上,利用散射域中的水平位移衰减函数,通过位移场的叠加考虑桩-桩间的波动干扰和群桩效应,推导了水平稳态谐振下非饱和土中单桩及群桩基础的阻抗函数以及各单桩分担的荷载,并讨论了饱和度、频率和桩间距等参数对基础振动特性的影响。
(5)推导了两种不混溶流体饱和多孔介质中Rayleigh波的弥散特征方程,讨论了波速、自由场位移分布及粒子运动轨迹,随后在求得非饱和土半空间自由波场解的基础上,采用Winkler地基梁模型,考虑上部结构惯性力的作用,对频域内全埋入单桩和部分埋入单桩在Rayleigh波作用下的横向动力响应进行了研究,分析了饱和度、轴向荷载和自由段桩长等因素与桩的地震反应之间的相互影响关系。
(6)通过开展红黏土中单桩轴向循环荷载模型试验,对不同循环荷载比和加载频率下桩的长期动力特性进行了研究,并从桩侧土剪切刚度和侧阻退化两方面出发,对循环荷载作用下桩顶累积沉降机理进行了分析。在FLAC3D中,实现了能够反映剪切刚度疲劳退化的修正Hardin-Drnevich(H-D)模型,并对常法向刚度(CNS)循环剪切下侧阻退化进行了数值模拟。
Abstract:Pile dynamics is the theoretical basis of both seismic design for building supporting by piles and integrity testing of piles. Owing to the complexity of the problem, the soils were usually assumed to be single-phase or saturated two-phase elastic medium for simplicity in the past studies. As we know, the near-surface soil existing in engineering environment is mostly unsaturated, and consists of three-phase system: solid skeleton and pores, with water and air filled in the pores. Based on the theoretical framework of unsaturated soil, and following the motion equations for multiphase porous media, the soil-pile dynamic interaction, the fundamental solution of internal dynamic source in a semi-infinite unsaturated elastic medium, and the deformation characteristics of pile subjected to cyclic loading are investigated in this paper via analytical and experimental studies. The viscous and inertial couplings between each phase together with the capillary pressure are taken into account during the process of derivation. The main contents of this thesis are listed as follows:
(1) The three dimensional lamb's problem under consideration is to determine the motion of an unsaturated poroelastic half-space subjected to internal excitation. By the application of the techniques of Fourier expansion and Hankel integral transforms with respect to the circumferential and radial coordinates, respectively, the general solution of the governing partial differential equations in the transformed domain is obtained. Furthermore, the closed form Green's functions of an unsaturated homogeneous elastic half-space to an arbitrary internal harmonic loading is derived, with consideration of the boundary conditions of the surface and the continuity conditions at the depth of loading. The formulas developed are confirmed in comparison with the degenerated solution of saturated soil.
(2) Considering the effect of matric suction on the dynamic shear modulus, the interaction model between the unsaturated soil and single pile under vertical harmonic motion is proposed. The resistance factor and vibration modes of soil layer are first obtained from the direct decoupling of the governing equations under axisymmetric conditions. On the basis of the assumptions of perfect contact along the pile-soil and the supporting types at the pile tip (rigid bearing or Winkler model), the motion equation of the pile treated as a bar and described by the conventional1-D structure vibration theory is then solved. The complex stiffness at the top of the pile, the velocity mobility together with the soil impedances in the frequency domain are derived ultimately.
(3) By virtue of the Helmholtz decomposition and variable separation method to the decoupling of motion equation, the dynamic characteristics for the horizontal vibration of an end-bearing pile in unsaturated soil are investigated through the three-dimensional continuum model proposed by Novak. The bending, shearing effects of pile are accounted for by modeling the pile as a Timoshenko beam. Moreover, utilizing the dynamic Green's function for unsaturated half-space under interior horizontal disk loading, the second kind of Fredholm integral equations describing the dynamic response of the laterally loaded single pile are established via the fictitious pile method. The semi-analytical solutions for dynamic stiffness of the pile head are developed in the frequency domain, and the distributions of pile displacement, bending moment and shear force along the depth are examined.
(4) With the Novak plain strain model, approximate dynamic impedance of single pile subjected to lateral vibration is first derived within the framework of wave theory of three-phase porous medium. A modified attenuation function of horizontal movements in scattering domain is then obtained, and the response of single pile is further extended to pile groups by employing the principle of superstition based on pile-pile interaction factor. On the basis of the developed solutions, the effects of parameters including the saturation, the excitation frequency and the pile spacing on the dynamic behavior as well as the load sharing are studied.
(5) The dispersion equations of Rayleigh waves in a porous medium saturated by two immiscible viscous fluids are deduced, and the variations of wave velocity, displacement distribution of free field and particle motion are discussed with the changes of soil properties. And then, considering the inertia effect of the superstructures, and within the obtained wave field solution for unsaturated soil half space, closed-form expressions for transverse seismic performance are presented through a dynamic Winkler model, for both fully-buried and partially-buried single pile in the unsaturated soil excited by incident Rayleigh waves. In addition, the influences of the saturation, the axial loading and the pile length of extended segment on the seismic response of pile are determined through numerical calculation.
(6) The performance of small-scale model piles embedded into red clay and tested under cyclic axial loadings is presented. The influences of cyclic loading levels and rates on long-term dynamic behaviors of pile are observed, and the mechanics of accumulated settlement is analyzed from the views of shear stiffness softening and skin friction degradation. Furthermore, the modified Hardin-Drnevich (H-D) model, being capable of reflecting the fatigue degradation of shear stiffness, is achieved in the FLAC3D, and the behavior of shear resistance degradation during quasi-static cyclic shearing under constant normal stiffness (CNS) condition is numerically investigated.
引文
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